Mr Shearer said it was possible Mr Horomia had looked for a successor.
"What I would like to do is have a look at who is around. Obviously Parekura's recommendation is hugely important, but we want to have a fair process like we always do."
It is understood one of those Mr Horomia favoured was Mr Hape, from Dannevirke and in his mid-30s. Mr Hape told the Herald he did not want to comment because it was a time to farewell Mr Horomia.
Other names mentioned have included Meka Whaitiri, the chief executive of Ngati Kahungunu, who worked for Mr Horomia when he was Minister of Maori Affairs. She is believed to be reluctant to stand.
Mr Horomia had also spoken to Te Karere presenter Scotty Morrison about running - but Mr Morrison said he was not interested for now because he had a young family. He ruled out the Ikaroa-Rawhiti byelection because he did not have the iwi links.
"I think they will be looking for someone who is tribally connected. It would be very hard to try and win that seat without being connected."
Mr Jones said it was almost certain to be a person who had the right iwi links for the electorate, which is predominantly Ngati Porou and Ngati Kahungunu.
Former Labour MP Dover Samuels said Labour should pay heed to what Mr Horomia had wanted.
"He did tremendous work for his people, and really Labour has to take direction from him in terms of his legacy. Not only was he a big man with big boots to fill, so was his mana and he talked a lot with some about the fact he hadn't completed his dreams and what he wanted."
The Mana and Maori Parties are waiting until after the tangi ends on Saturday to decide whether to enter the byelection and if so, who to stand.
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